David Lewis's Metaphysics

First published Tue Jan 5, 2010

David Lewis produced a body of philosophical writing that, in four
books and scores of articles, spanned every major philosophical area,
with perhaps the greatest concentration in metaphysics, philosophy of
language, philosophical logic, and philosophy of mind. Despite this
astonishing variety, a newcomer to Lewis's philosophy would be best
advised to begin with his metaphysics (especially: 1986a, 1986e,
1999). There are several reasons. First, the majority of Lewis's work
either concerns, or substantially overlaps, topics in
metaphysics. Second, the metaphysical positions Lewis stakes out are
strikingly original and powerfully argued. Third, there is a coherence
and systematicity to this work that makes it a particularly
appropriate object for study, in that one sees trademark Lewisian
philosophical maneuvers clearly on display. (Indeed, if one wished to
learn how to do philosophy in a Lewisian style, the most efficient way
to do so would be to study his work in metaphysics.) Finally, and
perhaps most interestingly, Lewis's metaphysics exerted a profound
regulating influence on the rest of his philosophy: if some otherwise
attractive position on some philosophical problem could not be made to
square with his overall metaphysical outlook, then it would have to be
abandoned.

I should forestall one possible misunderstanding. You might think
that, given what I've just said, the way Lewis would recommend
doing philosophy is as follows: First you figure out what your basic
metaphysical commitments should be; then you turn your attention to
various broad but non-foundational philosophical subject matters
(personal identity, mental content, the nature of knowledge, theory of
value, etc.), and work out the consequences in each of these arenas of
your fundamental metaphysical posits. Nothing could be further from
Lewis's preferred methodology. (Well, maybe relying on divine
revelation would be further….) What he in fact recommends is a
holistic approach: we start with the total body of claims we are
inclined to believe—whether on the basis of “common
sense” (an oft-invoked category, for Lewis) or of
science—and try our best to systematize it in accordance
with standards of theoretical goodness that are themselves endorsed by
common sense and/or science (and so are themselves, to some extent,
also up for grabs). A substantial portion of Lewis's overall body
of philosophical work can thus be seen as an extended—and
breathtakingly ambitious—attempt at achieving total
reflective equilibrium. Here is an especially succinct description
of this approach:

One comes to philosophy already endowed with a stock of opinions. It
is not the business of philosophy either to undermine or to justify
these preexisting opinions, to any great extent, but only to try to
discover ways of expanding them into an orderly system. (1973b, p.
88)

Still, while Lewis's method of philosophical inquiry is certainly not
“bottom-up”, in my opinion it is best to present
the results of that inquiry in a bottom-up fashion. That is
what this essay, and ones to follow, will attempt to do. I will divide
the terrain into four parts: Lewis's fundamental ontology; his theory
of metaphysical modality; his “applied” metaphysics
(covering such topics as laws of nature, counterfactuals, causation,
identity through time, and the mind); and Lewisian methodology in
metaphysics. I'll explain these distinctions shortly, but be advised
that the present essay will almost exclusively address the first of
these four topics. Other aspects of Lewis's thought are covered
in the general entry on
David Lewis.

On a traditional conception, metaphysics aims to answer, in a
suitably abstract and fully general manner, two questions:

What is there?

What is it (that is, whatever it is that there is) like?

Lewis fully endorses this conception: for him, metaphysicians are
not in the business merely of analyzing our “conceptual
scheme” (except insofar as doing so is an effective
method for finding answers to metaphysical questions), nor
need they pay any heed to the perennial philosophical calls for the
abolition of their subject. They are, rather, engaged in an
unproblematically factual inquiry into the nature of reality—one
whose recognizable epistemological pitfalls provide no grounds for
doubting its legitimacy:

Once the menu of well-worked-out theories is before us, philosophy
is a matter of opinion. Is that to say that there is no truth to be
had? Or that the truth is of our own making, and different ones of us
can make it differently? Not at all! If you say flatly that there is no
god, and I say that there are countless gods but none of them are our
worldmates, then it may be that neither of us is making any mistake of
method. We may each be bringing our opinions to equilibrium in the most
careful possible way, taking account of all the arguments,
distinctions, and counterexamples. But one of us, at least, is making a
mistake of fact. Which one is wrong depends on what there is. (Lewis
1983a, p. xi)

We can begin to get a handle on Lewis's audacious and
comprehensive answers to our two overarching questions by
distinguishing three components to his metaphysical program:

First, he offers an account of what the fundamental ontological
structure of the world is. Is, and must be—although
as we'll see, that qualification turns out to be in a certain
sense trivial. This account of fundamental ontology of course
presupposes that the word “fundamental” means
something, and in particular manages to cleanly distinguish a certain
central core of one's ontological commitments from the rest.
Suppose these commitments take the form of views about what entities
(or “particulars”) there are, and what properties and
relations they stand in. Then we can distinguish two questions. Are
some entities more fundamental than others—with, perhaps, an
elite group of entities being the most fundamental? Are some
properties/relations more fundamental than others—again, with,
perhaps, an elite group being the most fundamental? You might find a
“yes” answer to both questions attractive. (E.g., chairs
exist, but they are not fundamental-level entities—though perhaps
quarks are. Likewise, some chairs have the property of being made
of oak; but this is not a fundamental-level property—though
perhaps the property of having such-and-such electric charge is.) As
for Lewis's own views, with respect to the second question they
are fairly unambiguous: He is quite clear that a proper ontology must
include not just particulars but also properties and relations (see
especially 1983b); he is equally clear that it is a perfectly objective
and determinate matter which of these properties/relations are more
fundamental (or, in his terminology, more “natural”) than
others (ibid.); he is officially agnostic about whether some
properties/relations are most fundamental, or
perfectly natural (1986f). His views on the first question
are, to my eyes at least, more difficult to discern—but for
reasons that, in the final analysis, probably do not
matter. See the

What's more, to a very great extent he takes it that the route
to a proper theory of fundamental ontology is by way of a priori
philosophical inquiry. (An important qualification will be noted
shortly.)

Second, he offers an account of modality, his famous
“realism” about possible worlds. Lewis, like many
philosophers, takes talk of possibility and necessity to be best
explicated as disguised quantification over possible worlds (and
possible inhabitants thereof), and he was endlessly ingenious at
showing how to use the resources provided by a theory of
“possibilia” to produce analyses of a host of modal
locutions. But his realism about possible worlds consists in much more
than inclusion of such entities into his ontology; indeed, it would
probably be better to call Lewis a “reductionist” about
modality—reductionist in a way that distinguishes him from
virtually every other philosopher of modality. For a typical believer
in possible worlds will, if asked to explain what they are, give an
account that uses modal notions at some crucial point. Perhaps
she will say that possible worlds are maximal consistent sets
of sentences (in some appropriate language); or perhaps she will say
that they are certain kinds of maximal properties that reality as a
whole could have instantiated. Lewis says no such thing: he
offers a characterization of possible worlds—and thus of modality
generally—in explicitly non-modal terms. This complete
subordination of the modal to the non-modal gives his philosophy of
modality a quite radical character, and also sheds light on some of his
seemingly independent views about the modalities involved in such
concepts as causation, law of nature, and chance. (For example, Lewis
rejects philosophical accounts of laws of nature that rely on any
primitive modal notions.)

Third, Lewis offers an account of how facts about everything else
reduce to the sorts of facts laid out in his accounts of
fundamental ontology and modality. (Note that given the remarks in the
last paragraph, these reductions ultimately rest on facts about
fundamental ontology alone; no unanalyzed modal notions are
involved in them.) Better: he offers an assortment of distinctive
approaches for constructing such reductions, of which there are many
examples but no single, canonical exposition. At this point I wish to
make just three observations about these strategies. First, they can be
seen to be directed at providing answers to a distinctively
metaphysical kind of question, of the form, “What is it for
such-and-such a fact to obtain?” Examples will pin down the
idea:

Question: What is it for an object to persist through time?
Lewis's answer: It is for that object to be constituted by
three-dimensional, instantaneous time-slices that exist at different
times. (Lewis 1988)

Question: What is it for an object to have a certain property
essentially? Lewis's answer: It is for every one of that
object's counterparts in other possible worlds to have that
property. (Lewis 1968)

Question: What is an event? Lewis's answer: It is a certain
kind of property of spacetime regions. (Lewis 1986d)

Question: What is it for one event to be a cause of another?
Lewis's (preliminary) answer: It is for the second event to
counterfactually depend on the first, in the sense that had the first
not occurred, the second would not
have.[1]
(Lewis 1973a, 1986b)

Question: What is an explanation of some event? Lewis's
answer: It is a quantity of information about that event's
causes. (Lewis 1986c)

And so on. It is this kind of question—albeit not always
phrased in this way, and accompanied by definite views about what
constitutes a philosophically appropriate answer—that animate
what we might call Lewis's “applied metaphysics”: the
application of his basic positions in ontology and modality to a range
of perennial metaphysical topics. Note that the reductionist
character of his approach comes out when we pursue the obvious
follow-up questions: For example, what is it for one event to
counterfactually depend on another? Roughly, it is for the closest
possible world in which the second does not occur to be a world in
which the first does not occur. What is it for one world to be closer
to actuality than another? We'll skip the answer for
now—but rest assured that it and the answers to subsequent
follow-up questions are designed to hang together in such a way as to
collectively display how facts about what causes what ultimately reduce
to facts about fundamental ontology. And so it goes, for personal
identity, free will, the mind, knowledge, ethics, laws of nature, you
name it.

The second observation is that it remains far from clear whether we can
dispense with the notion of “reduce to” (or
“determined by”, “fixed by”, etc.) in favor of
some philosophically more sanitized alternative;
see the

The third observation I wish to make at this point is that Lewis is
strongly motivated by a desire for theoretical economy—both with
respect to ontology and with respect to ideology. His quest for
ontological economy shows up in the austerity of the kinds of
fundamental entities he admits into his ontology (he neither shows, nor
cares to show, any economy with respect to their number). His
quest for ideological economy shows up in several places, but perhaps
most notably in his utter rejection of any unanalyzed modal
notions, and—something that hasn't been mentioned
yet—in his attempted reduction of set theory to mereology and
plural quantification. More on this in the (forthcoming) article on his
applied metaphysics, as well as other examples of his focus on
ideological parsimony at work.

Let's take a somewhat closer look, now, at Lewis's
account of fundamental ontology.

It will be useful to start with a view that is almost
Lewis's—almost, but not quite, as it is more opinionated
than he would be comfortable with. Stating the view takes but a few
lines; providing the needed commentary will take longer. Thus,
Almost-Lewis says the following:

The only fundamental entities that are particulars
are spacetime points.

What these particulars are like is given by what perfectly
natural monadic properties they instantiate, and what perfectly natural
relations they stand in to one another.

And that's it. That is, the facts about what fundamental
particulars there are, and what perfectly natural properties and
relations they instantiate, determine all other facts. Yes, even modal
facts, as the (forthcoming) companion article explains. Almost-Lewis
(and Lewis) believes, of course, in other particulars besides
spacetime points; it's just that these particulars are not
fundamental: what it is for them to exist is to be explained, somehow,
in terms of facts about the fundamental entities. (More on this, in the
forthcoming companion article on Lewis's applied metaphysics;
also, see the

Notice one consequence: If the facts about what fundamental
particulars there are, and what perfectly natural properties and
relations they instantiate, determine all other facts, then
there is no reason to suppose that composite
particulars—particulars that have other particulars as proper
parts—ever instantiate perfectly natural monadic
properties. (Of course, they can perfectly well instantiate the
very-but-not-perfectly natural property of having parts that
instantiate such-and-such a perfectly natural relation.) Thus,
if, for example, my laptop has a mass of 3 kg, that is so only in a
slightly derivative sense: the laptop is composed of parts whose masses
add up to 3 kg.

As noted, the position of Almost-Lewis is not that of
Lewis, and shortly we will need to review the key respect in which, by
Lewis's lights, it overreaches. But first we need to elaborate
and clarify the content of Almost-Lewis's position, by means of
some commentary.

Four questions demand attention: What are “perfectly
natural” properties and relations? What does it come to to say
that the fundamental particulars are spacetime points? What
does it come to to say that they are spacetime points?
Finally, what is the relationship between the fundamental ontology
posited by Almost-Lewis and Lewis's own celebrated thesis of
Humean Supervenience? Let's consider these topics in turn.

Remember that laying out the foundations of one's ontology
requires two things: to say what, fundamentally, there is; and
to say what it is like, presumably by stating some facts
about the fundamental entities. But not just any facts matter. For
example, it may be true of some of the fundamental entities that they
coexist with at least one pig; but saying so does nothing to help
articulate the fundamental structure of reality. To do that,
Lewis thinks, one needs a distinction among the properties and
relations: some are special, in that it is their pattern of
instantiation among the fundamental entities that constitutes the
fundamental structure of reality—the “joints” along
which nature is to be ultimately carved. These special properties and
relations are the “perfectly natural” ones.

(There are a variety of other uses to which Lewis puts the notion of
“natural” properties, some of which show that what he needs
is a distinction that admits of gradations, with the perfectly
natural properties at one extreme. Many of these additional uses will
be mentioned in the (forthcoming) article on his applied metaphysics;
but see the

It is not enough merely to appeal to such a distinction;
for metaphysics to do its job properly, it must also provide an
account. Now, one way to proceed would be to provide a theory
of what properties and relations are, in which it is stipulated that
all such things are to count as “perfectly natural”. On
such an approach, while there may well be a property corresponding to
the predicate “has mass 5 kg” (for example), there will
almost certainly be no property corresponding to the predicate
“is green” (let alone that familiar gerrymander, “is
grue”). Lewis favors a different approach. Given his commitment
to set theory, he already believes in things that, by his
lights, deserve to be called the property of being green, and indeed
the property of being grue: these are merely certain
sets—sets of actual and possible objects. (See the
section on Lewis' modal metaphysics in the entry on
David Lewis,
and the supplement on
The Natural/Non-natural Distinction.)
The question for him, then, is
how to distinguish among these sets those that are perfectly
natural. Here I will present Almost-Lewis as being, almost like Lewis,
agnostic as between four broad alternatives. (Almost, because Lewis
eventually decided that the first alternative, according to which
natural properties and relations are Aristotelian universals, is
unworkable; see his 1986f for the reasons.)

One could adopt a theory of universals of the kind
developed by David Armstrong (1978a,1978b): “…we could
call a property [viz., set of actual and possible objects]
perfectly natural if its members are all and only those things
that share some one universal.” (1999 p. 13)

One could treat “natural” as a primitive
predicate of sets of actual and possible objects: “…a
Nominalist could take it as a primitive fact that some classes of
things are perfectly natural properties; others are less-than-perfectly
natural to various degrees; and most are not at all natural. Such a
Nominalist uses ‘natural’ as a primitive predicate, and
offers no analysis of what he means in predicating it of
classes.” (1999, p.
14)[2]

One could define “natural” in terms of a suitably
complex, and primitive, notion of resemblance:
“Alternatively, a Nominalist in pursuit of adequacy might prefer
to rest with primitive objective resemblance among things. …Then
he could undertake to define natural properties in terms of the mutual
resemblance of their members and the failure of resemblance between
their members and their non-members.” (1999, p. 14)

One could adopt an ontology of tropes—roughly,
property-instances, entities that occupy a sort of ontological halfway
house between particulars and properties. (See Lewis 1986f, Williams
1953, Campbell 1990.)

Returning now to Almost-Lewis's fundamental ontology, the
options seem to be these: It might be that a spacetime point (or
sequence of points) instantiates a perfectly natural property
(respectively, relation) by instantiating a universal, in the sense of
Armstrong. It might be that it has it by having as one part a certain
kind of trope, in roughly the sense of Williams. (Whence we must amend
slightly, and take these tropes to be the fundamental
entities.) It might be that it has it by belonging to a special sort of
set of (actual and merely possible) spacetime points—special
either on account of the resemblances that unite its members and
distinguish them from non-members, or on account of simply being
perfectly natural. Regardless of which one chooses, Lewis thinks,
one's theory of natural properties and relations ought to respect
four philosophically-motivated constraints:

First, an adequate theory should be minimal, in
the sense that it posits just enough perfectly natural properties and
relations for their distribution among the fundamental particulars to
fully and determinately fix the nature of all of reality: “The
guiding idea, roughly, is that the world's universals should
comprise a minimal basis for characterizing the world completely.
Universals that do not contribute at all to this end are unwelcome, and
so are universals that contribute only redundantly.” (1999, p.
12) It is clear from the surrounding text that Lewis takes this
constraint to govern the various alternatives to a universals account
of
naturalness.[3]

Second, perfectly natural properties and relations are, Lewis
thinks, non-modal. What, exactly, this means will need to come
in for more discussion in the (forthcoming) companion article on
Lewis's applied metaphysics, where we discuss his views about
laws of nature and related nomological concepts. For the moment, we can
take it to mean roughly this (though trouble for this characterization
quickly arises): the instantiation of a perfectly natural property by
one (fundamental) particular, or of a relation by several, places
absolutely no constraints of a logical or metaphysical kind on the
instantiation of any other perfectly natural property or relation by
that or any other particular or particulars.

Third, they are intrinsic to the particulars that
instantiate them—which, all too roughly, means that they
characterize what those particulars are like, independently of what any
other distinct particular is like. More: The intrinsic nature of any
particular is exhausted by what perfectly natural properties
it
instantiates.[4]
This assumption also allows a theory of natural properties and
relations to yield, in a fairly simple way, a definition of
“perfect duplicate” applicable to any possible objects x
and y (not necessarily inhabiting the same possible world): x and y are
perfect duplicates iff they share exactly the same perfectly
natural
properties.[5]
A
definition of “intrinsic” follows: a property P is
intrinsic iff any two duplicates x and y (taken from any possible
worlds) either both have P or both fail to have P. Of course, what we
really have here is a tight circle that puts on display how the
expressions “intrinsic”, “perfect duplicate”,
and “perfectly natural” can be interdefined, with the help
of the modal notion of metaphysical possibility. (See Lewis 1983c and
Langton & Lewis 1998 for discussion of various strategies for
breaking out of this circle.)

The fourth constraint is purely negative: it is that it should be
left to the empirical sciences to fill in the details about
which perfectly natural monadic properties there are
(at least, in actuality: philosophy might teach us, or at
least give us some reason to believe, that there are, in other possible
worlds, so-called “alien” properties, perfectly natural
properties not instantiated in the actual world). Not just any
empirical science will do: given, in particular, the first of the four
theses, it is really the job of fundamental physics to fill in these
details. The special sciences get no say.

What about perfectly natural relations? Here matters are less clear.
Lewis certainly thinks that spatiotemporal relations are perfectly
natural; what is less obvious is whether, by his lights, physics could
rationally lead us to reject this claim. For now I will
simplify, and have Almost-Lewis add a fifth
constraint—one that is in tension at least with the spirit of the
fourth, and that the real Lewis certainly rejects. It is this: not only
are spatiotemporal relations perfectly natural, they are the
only perfectly natural relations. (The only possible
ones—though remember that given Lewis's reductionism about
modality, that is an idle addition.)

The picture that emerges is this: Reality consists of a multitude of
spacetime points. Each of these stands in spatiotemporal relations to
some others (though not to all others: see the companion
article on Lewis's theory of modality). Each instantiates various
perfectly natural, non-modal monadic properties. That is all there is;
anything putatively “extra”—facts about laws of
nature, or about persisting macro-objects, or about causation, or about
mentality, or about ethics, or about sets, etc.—must somehow
reduce to that stuff. For Almost-Lewis, this picture captures a
fundamental truth about the nature of existence. It is roughly right
that it is also a necessary truth—a status that would
seem to fall out automatically, given Lewis's reductionist
account of modality. (We will see, in the companion article, reasons
for thinking that he is better off simply dismissing any
questions about the modal status of his theses about fundamental
ontology.) The only unfinished philosophical business is to
work out the right theory of natural properties and relations, and to
work out the details of the reduction for particular cases.

The foregoing Almost-Lewisian thesis about spatiotemporal relations
is too strong to be tenable: we now have reasonably good reasons, drawn
from quantum physics, for holding that even in the actual world, there
are perfectly natural relations other than the purely spatiotemporal
ones. (Roughly: the relations—whatever exactly they amount
to—coded up in the quantum mechanical wave-function.) Two points
in its defense are, however, worth brief mention: First, seemingly
obvious counterexamples—involving such basic physical relations
as being more massive than—in fact aren't
counterexamples, since Lewis can deny that they are genuinely
fundamental or perfectly natural, on the basis that facts
about their obtaining reduce to facts about the distribution of monadic
perfectly natural properties. (Still, they will certainly turn out to
be very natural.) Second, if we could at least maintain, as a
contingent thesis, that the only perfectly natural relations
are spatiotemporal ones, then we could plausibly settle an unresolved
and deeply vexed question about the content of physicalism (the
doctrine, to put it rather too crudely, that all there is to the actual
world is physical stuff), as explained in the

At any rate, the thesis that spatiotemporal relations are at least
among the perfectly natural relations allows us to clarify and
simplify Almost-Lewis's position. Specifically, we can say that
all that it comes to to say that the fundamental entities are
spacetime points is that they stand in perfectly natural
spatiotemporal relations to one another.
For more, see the

To say that they are spacetime points, finally, is to say
that they have no proper parts.

One upshot is that my original statement of Almost-Lewis's
ontology needs an amendment: for it was misleading to say that
according to him, the fundamental particulars are spacetime
points. That's true, but it wrongly suggests that he is making a
choice of one fundamental kind of particular, distinguished
from other possible choices by the essential nature of its members. Not
so. It is more accurate to describe his fundamental ontology thus:

There are particulars.

They are, or are wholly composed of,
simples—particulars have no other particulars as proper
parts.

Almost-Lewis's theses about what fundamental ontology
comprises, and how all other facts reduce to facts about it, bears a
very close relationship to Lewis's celebrated thesis of Humean
Supervenience (hereafter: “HS”). But they are not the same,
and the differences are worth keeping track of. Here is a typical
statement of HS (slightly stronger, as we'll see, than the
version Lewis officially endorses): No two possible worlds differ with
respect to what is true at them, without differing with respect to the
geometrical arrangement of their spacetime points, or with respect to
which perfectly natural properties are instantiated at those
points.[6]
(Note that so
stated, HS is automatically metaphysically necessary.) Thus,
HS is a supervenience claim, logically weaker than
Almost-Lewis's claim of reduction. It is also a claim
that—for some good reasons and some bad reasons—Lewis
accepts only in a weaker form that is metaphysically
contingent. More significantly, it is no part of HS that facts
about possible worlds themselves reduce to anything else;
whereas both Almost-Lewis and Lewis are explicit in their commitment to
this further claim. Having said all this, it will be worth remembering
in what follows that Almost-Lewis's position (which, remember,
incorporates Lewis's modal realism) entails HS. So, any
doubts about HS will carry over to Almost-Lewis's fundamental
ontology.

Second, Lewis is agnostic as to whether, in addition to spacetime
points, there might be (in this, or other possible worlds) fundamental
entities that are occupants of such points. But agnosticism on
this score is probably a bad idea: the proposed possibility is not
clearly intelligible, nor it is clear what its motivation could be.
For more, see the

Third, on a plausible story about what non­-fundamental
entities there are, it will turn out that on Almost-Lewis's view,
everything that exists is composed of simples (parts, that themselves
have no proper parts). Lewis is also agnostic on this score: he takes
it to be at least an epistemic possibility that there is
“gunk”: something, every proper part of which itself has a
proper part (see for example Lewis 1991). Lewis says relatively little
either about the status of this possibility (in particular, is it more
than merely epistemic?), or about its potential ramifications for his
various positions in metaphysics. To keep things simple, I will
discount it for the remainder of this main essay.

Fourth, Lewis holds that his thesis of Humean Supervenience is, at
best, only contingently true. Of course, given that he
recognizes the (metaphysical) possibility of perfectly natural,
non-spatiotemporal relations, he should treat HS as at best
contingent. But he advances reasons for doing so of a quite different
sort. They are not particularly good reasons, and so we will pass them
by; but see the

What, finally, should we make of Lewis's conception of
fundamental ontology? A complicated question; I will limit discussion
to just two important worries. Let's begin by noting the obvious
influence of a certain scientifically-informed conception of the world
in shaping Lewis's picture of reality. Lewis himself is quite
explicit about this influence:

The picture is inspired by classical physics. Humean Supervenience
doesn't actually say that physics is right about what local
qualities there are, but that's the case to keep in mind. But if
we keep physics in mind, we'd better remember that physics
isn't really classical. …The point of defending Humean
Supervenience is not to support reactionary physics, but rather to
resist philosophical arguments that there are more things in heaven and
earth than physics has dreamt of. (1994, p. 474)

But there is a less acknowledged influence of first-order
predicate logic—an influence that is not entirely salutary. It is
undoubtedly tempting, for philosophers steeped in the use of
first-order logic as a clarifying tool, to assume that the proper
representation of the ultimate structure of reality must be by means of
some (interpreted) first-order language—a language whose various
predicates could be taken to express the various
fundamental properties and relations that characterize reality
at its most basic level. But if we look to physics instead—as we
surely ought to—we find that the basic representational tools are
variables, that correspond to physical magnitudes.
Taking seriously the picture of fundamental ontology suggested by these
representations turns out to matter quite a bit: in particular, there
are reasons to think that none of the first three theses about natural
properties and relations—that they are minimal, non-modal, and
intrinsic—is tenable without some modification. This
issue—which we will mostly pass over in what follows, except
where it matters—is explored in more detail in the

The second significant source of concern about Lewis's
conception of fundamental ontology is the role—or rather lack
thereof—that modal notions have in it. This concern has
two aspects. First, one might hold that some, at least, of the
fundamental properties and relations that characterize reality have
modal aspects that are ontologically basic. Consider mass: one
might hold that it is metaphysically impossible for there to be a world
containing just two massive particles, accelerating away from each
other—and that this impossibility somehow flows from the nature
of mass itself. We will take up this issue in more detail in the
companion article on Lewis's applied metaphysics.

Second, one might hold that it is one thing to state a thesis
concerning what the fundamental structure of reality in fact
happens to be; but that it is another, separate matter to
state how reality could be. Indeed, most metaphysicians, I
suspect, take it to be just blindingly obvious that these are
conceptually distinct tasks. Granted that one's views on what
there is, and what it is like, will have ramifications for one's
views on what there could be and what it could be
like (most obviously, because things could be the way they
are; but there may be more interesting and subtle connections
as well); still, the project of laying out the former views does not
automatically complete the project of laying out the
latter.

Of course there is a sense in which Lewis agrees: he takes it as
obvious, after all, that he must supply an account of modality. But the
strikingly reductionist character of that account shows that such
agreement as there is is mighty thin. The next article (forthcoming)
will help clarify this quite radical aspect to Lewis's
metaphysics.